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Chapter 24: Q86P (page 716)

Figure 24-68 shows a hemisphere with a charge of 4.00μC distributed uniformly through its volume. The hemisphere lies on an xy plane the way half a grapefruit might lie face down on a kitchen table. Point P is located on the plane, along a radial line from the hemisphere’s center of curvature, at radial distance15cm .What is the electric potential at point P due to the hemisphere?

Short Answer

Expert verified

The electric potential at point P isV=0.24MV

Step by step solution

01

Step 1: Given data:

The charge on the hemisphere,q=4.0μC=4.0×10−6C.

The radius of the curvature, R=15cm=0.15m.

02

Determining the concept:

The electric potential at point P will be the same as on its surface because the charges are uniformly distributed.

Formula:

The potential is define by,

V=14πεo⋅qR=kqR

Here, ε0 is the permittivity of free space, q is the electron charge, and R is the distance, and k is the Coulomb’s constant having a value 9×109Nm2/C2.

03

Determining the electric potential:

Write the equation for the potential as below.

V=k⋅qR

Substitute known values in the above equation.

V=(9×109Nm2/C2)×4.0×10−6C0.15m=2.4×105V=0.24MV

Hence, the electric potential is 0.24MV.

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Most popular questions from this chapter

Question: What is the escape speedfor an electron initially at rest on the surface of a sphere with a radius ofand a uniformly distributed charge of1.6×10-15C? That is, what initial speed must the electron have in order to reach an infinite distance from the sphere and have zero kinetic energy when it gets there?

Proton in a well.Figure 24-59shows electric potential Valong an xaxis.The scale of the vertical axis is set by Vs=10.0 V. A proton is to be released at x=3.5 cmwith initial kinetic energy 4.00 eV. (a) If it is initially moving in the negativedirection of the axis, does it reach a turning point (if so, what is the x-coordinate of that point) or does it escape from the plottedregion (if so, what is its speed at x=0)? (b) If it is initially movingin the positive direction of the axis, does it reach a turning point (ifso, what is the xcoordinate of that point) or does it escape from theplotted region (if so, what is its speed at x=6.0 cm)? What are the (c) magnitude Fand (d) direction (positive or negative direction ofthe xaxis) of the electric force on the proton if the proton movesjust to the left of x=3.0 cm? What is (e) Fand (f) the direction ifthe proton moves just to the right of x=5.0 cm?

Question: How much work is required to set up the arrangement of Fig. 24-52 if, q =2.30 pC, a = 64.0 cm and the particles are initially infinitely far apart and at rest?

A uniform charge of 16.0μCis on a thin circular ring lying in xy plane and centered on the origin. The ring’s radius is3.00cm. If point A is at the origin and point B is on the z-axis at z=4.00cm, what isVB-VA?

Question: Figure 24-45 shows a thin rod with a uniform charge density of2.00μc/m. Evaluate the electric potential at point Pifd=D=L/4.00. Assume that the potential is zero at infinity.
See all solutions

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